The present invention relates generally to methods for evaluating nuclear power core operation, and more particularly to an improved method and apparatus for determining an operating limit minimum critical power ratio (OLMCPR) so as to effectuate increased efficiency and operation of Boiling Water Reactors (BWR).
A Boiling Water Nuclear Reactor (BWR) generates power from a controlled nuclear fission reaction. As shown in FIG. 1, a simplified BWR includes a reactor chamber 101 that contains a nuclear fuel core and water. Generated steam is transferred through pipe 102 to turbine 103, where electric power is generated, then water returns to the core through pipe 104. As shown in FIG. 2, the core 201 is made of approximately five hundred (500) bundles 202 of fuel rods arranged in a specific manner within the reactor core. As shown in FIG. 3, each bundle 301 contains roughly one hundred (100) fuel rods 302. Water in the core surrounds the rods. Heat generated by a nuclear reaction is transferred from the rods to the water circulating through the core, boiling some of the water. The heat generated in the core is carefully controlled to maintain safe and efficient reactor operations.
In a Boiling Water Nuclear Reactor there are basically three modes of heat transfer that must be considered in defining thermal limits for the reactor: (i) N ideate boiling, (ii) transition boiling and (iii) film boiling. xe2x80x9cNucleate boilingxe2x80x9d is the preferred efficient mode of heat transfer in which the BWR is designed to operate. xe2x80x9cTransition boilingxe2x80x9d is manifested by an unstable fuel rod cladding surface temperature which rises suddenly as steam blanketing of the heat transfer surface on the rod occurs, then PS to the nucleate boiling temperance as the steam blanket is swept away by the coolant flow, and then rises again. At still higher fuel rod/bundle operating powers, xe2x80x9cfilm boilingxe2x80x9d occurs which results in higher fuel rod cladding temperatures. The cladding temperature in film boiling, and possibly the temperature peaks in transition boiling, may reach values which could cause weakening of the rod cladding and accelerated corrosion. Fuel rod overheating is conservatively defined as the onset of the transition from nucleate boiling to film boiling. The conventional basis for reactor core and fuel rod design is defined such that some xe2x80x9cmargin,xe2x80x9d accommodating various design and operational xe2x80x9cuncertainties,xe2x80x9d is maintained between the most limiting operating condition and the transition boiling condition at all times for the life of the core.
The onset of transition boiling can be predicted by a correlation to the steam quality at which boiling transition occurs-called the xe2x80x9ccritical quality.xe2x80x9d Steam quality can be readily measured and is generally a function of measuring distance above the boiling boundary (boiling length) for any given mass flow rate, power level, pressure and bundle flow geometry among other factors. A xe2x80x9ccritical powerxe2x80x9d is defined as that bundle power which would produce the critical quality of steam. Accordingly, a xe2x80x9ccritical power ratioxe2x80x9d (CPR) is defined as the ratio of the critical power to the bundle operating power at the reactor condition of interest. CPR is descriptive of the relationship between normal operating conditions and conditions which produce a boiling transition. CPR is conventionally used to rate reactor design and operation. To assure a safe and efficient operation of the reactor, the CPR is kept above a prescribed value for all of fuel assemblies in the core. Reactor operating limits are conventionally defined in terms of the most limiting fuel bundle assembly in the corexe2x80x94defined as the xe2x80x9cminimum critical power ratioxe2x80x9d (MCPR). Reactor operating limits are often stated in terms of MCPR.
In nuclear power generation engineering, it is widely recognized that there is a possibility, however small, that the occurrence of a reactor transient event combined with the various xe2x80x9cuncertaintiesxe2x80x9d and tolerances inherent in reactor design and operation may cause transition boiling to exist locally at a fuel rod for some period of time. Accordingly, MCPR operating limits are conventionally set in accordance with the United States Nuclear Regulatory Commission (USNRC) design basis requirement that transients caused by a single operator error or a single equipment malfunction shall be limited such that, taking into consideration uncertainties In the core operating state, more than 99.9% of the fuel rods are expected to avoid boiling transition during that error or malfunction. A safety limit minimum critical power ratio (SLMCPR) defined under current USNRC requirements as the MCPR where no more than 0.1% of the fuel rods are subject to boiling transition (also known as NRSBT for Number of Rods Subject to Boiling Transition). The corresponding OLMCPR describes the core operating conditions such that the MCPR is not lower than the SLMCPR to a cc in statistical confidence.
i. An Ideal Approach
In principle, the OLMCPR could be calculated directly such that for the limiting anticipated operational occurrence (AOO), less than 0.1% of the rods in the core would be expected to experience boiling transition. This approach is described in U.S. Pat. No. 5,912,933, by Shaug et at. The process involved is shown in FIG. 4, which depicts histogram 40 of rod CPR values 401 versus number of rods 402 at the specific CFR value. While the CPR value is usually associated with a fuel bundle, it actually refers to the limiting rod in a bundle. Each rod in the bundle has a CPR value at is determined by the local power distribution and relative position of the rod within e bundle (R-factor). The lowest CPR of any one rod in the bundle Is used to characterize the CPR for the entire bundle.
The CPR 401 for a given rod has an associated probability distribution function (PDF) which reflects the uncertainties in its determination. The PDF may be determined experimentally and is shown as an Experimental Critical Power Ratio (ECPR) distribution 410. Thus, if a nominal CPR value (411) is 1.0, then the PDF 410 of probable actual CPR values range from 0.90 to 1.10. The variability in the rod CPR values is due to uncertainties in the initial rod condition, i.e., uncertainties in the measurements of parameters at the reactor operating state (core power) and in the modeling of derived parameters (power distribution).
To take the effect of a transient event on the CPR values into account, a safety margin is introduced to CPR values by shifting the acceptable nominal CPR value 405 for the lowest rod CPR to a larger CPR value, i.e., 1.25. The ECPR histogram distribution 403 for the lowest CPR rod is thus shifted such that the entire CPR histogram is above a CPR value of 1.20, and well above a CPR value of 1.0. Moreover, the nominal CPR values 407 for rods other than the lowest CPR rod are above the nominal CPR value, e.g., 1.25, of the lowest CPR rod.
During a transient in rod operation, the histogram 407 of rod CPRs shifts to the left to lower CPR values, resulting in the histogram 408. With this shift, the xe2x80x9cnominalxe2x80x9d CPR value 406 during the transient is at the point, e.g., 1.05, where the minimum CPR value is reached during the transient. The limiting rod will have an associated PDF 404, which includes both the uncertainties in the initial rod conditions and xe2x80x9ctransient uncertainties.xe2x80x9d The maximum change in critical power ratio during the transient (xcex94CPR 409) includes uncertainties in the modeling of the transient, both the physical models and plant parameters.
Ideally, this transient xcex94CPR 409 and associated OLMCPR would be generated as shown in FIG. 5, and described as follows:
Step 1: Assume a set of base core operating conditions using the parameters to run the plant that generates a core MCPR equal to the OLMCPR, as shown by block 501.
Step 2: Using the parameters, such as core power, core flow, core pressure and others, that predict a general bundle CPR set forth in block 506, determine the MCPR for each bundle in the core, as shown by block 502.
Step 3: Using parameters, such as rod placement within each bundle and rod power, that change each bundle CPR into individual rod CPR values set forth in block 507, determine the MCPR for each rod in the core, as shown by block 503.
Step 4: Using the ECPR probability distribution, generated by Equations 1 and 2, set forth in block 508, determine the percentage of NRSBT in the core by summing the probabilities of each rod in the core that is subject to boiling transition, as shown by block 504. This summation is shown by Equation 3.                     ECPR        =                              (                          CriticalPower              ⁢                              xe2x80x83                            ⁢              Predicted              ⁢                              xe2x80x83                            ⁢              by              ⁢                              xe2x80x83                            ⁢              Correlation                        )                                (                          Measured              ⁢                              xe2x80x83                            ⁢              CriticalPower                        )                                              (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )                                          P          1                =                              P            ⁡                          (                              z                i                            )                                =                                    1                                                2                  ⁢                  π                                                      ⁢                                          ∫                                  z                  i                                ∞                            ⁢                                                e                                                            -                                              1                        2                                                              ⁢                                          u                      2                                                                      ⁢                                  ⅆ                  u                                                                                        (                  Equation          ⁢                      xe2x80x83                    ⁢          2                )                                          NRSTB          ⁢                      xe2x80x83                    ⁢                      (            %            )                          =                              100                          N              rod                                xc3x97                                    ∑                              i                =                1                                            N                rod                                      ⁢                          [                                                P                  1                                xc3x97                                  (                                      1                    ⁢                    Rod                                    )                                            ]                                                          (                  Equation          ⁢                      xe2x80x83                    ⁢          3                )            
Step 5: Vary the parameters set forth in blocks 506 and 507 for a set number of Monte Carlo statistical trials, as shown by block 505. Compile the statistics from all the trials from steps 2 through 4 to generate a probability distribution of NRSBT.
Step 6: Compare the value of NRSBT percentage to 0.1%, as shown in block 509. If the percentage is greater than 0.1%, reset the core parameters to different initial conditions in order to comply with the USNRC regulations, as shown in block 510. Similar to Step 1 and block 501, the new initial conditions are assumed to generate an OLMCPR. The determination of NRSBT restarts and loops until the value of NRSBT is equal to 0.1%. Similarly, if the percentage is less than 0.1%, the core parameters are reset to increase the value of NRSBT in order to operate the core more efficiently or with fewer effluents.
Step 7: If the percentage of NRSBT equals 0.1%, the assumed value of OLMCPR, which equals core MCPR, complies with the USNRC regulations, as shown by block 511. Accordingly, the operating core conditions are set as the assumed parameters.
Because of the computational difficulties and the need to evolve efficient algorithms, the ideal process outlined above has not been followed. The currently approved process and the new approach to determining the OLMCPR are described in the following sections.
ii. The USNRC Approved Approach
In the current process, the OLMCPR determination is divided into primarily two steps, as shown by FIG. 6. Using a process similar to the ideal process, first the SLMCPR is determined so that less than 0.1% of the rods in the core will be expected to experience boiling transition at this value. In other words, 99.9% of the fuel rods in the core will be expected to avoid boiling transition if the MCPR in the core is greater than SLMCPR. Second, the OLMCPR is then established by summing the maximum change in MCPR (xcex94CPR95/95) expected from the most limiting transient event and the SLMCPR.
Since FIG. 6 is similar to the FIG. 4, only a brief description of its components follows. Histogram 600 shows the number of rods at a specific CPR value 602 versus the corresponding CPR value 601. The histogram 608 results with the lowest CPR rod 607 at a value of, e.g., 1.05, which equals the SLMCPR 603. Limiting rod distribution 606 shows the uncertainty in determination of the limiting CPR rod 607. Similar to the ideal process, the SLMCPR 603 is determined when the percentage of NRSBT is equal to 0.1%.
However, unlike the ideal process, the current process is unable to fully predict and measure certain parameters, such as the power distribution within each bundle and the power distribution along each rod. Thus, the uncertainties in calculating the SLMCPR do not allow equating the OLMCPR with the SLMCPR. Accordingly, an error factor, xcex94CPR95/95 605, is linearly added to the SLMCPR 603 to determine the OLMCPR 609. xcex94CPR95/95 605 conservatively corrects for the inherent limitations in the calculation of the SLMCFR 603.
Using the currently approved process, the OLMCPR 609 is generated as shown in FIG. 7, and described as follows:
Step 1: Assume a set of base core operating conditions using the parameters to run the plant generates a core MCPR equal to the SLMCPR as shown by block 701.
Step 2: Using the parameters, such as core power, core flow, core pressure, bundle power and others, that predict a general bundle CPR set forth in block 706, determine the MCPR for each bundle in the core as shown by block 702. This process step has large uncertainties in predicting the bundle power, biasing the calculations.
Step 3: Using parameters, such as rod placement within each b die and rod power, which change each bundle CPR into individual rod CPR values set forth in block 707, determine the MCPR for each rod in the core, as shown by block 703. Individual rod power is difficult to measure; combining that uncertainty with bundle power distribution uncertainty serves to increase the uncertainty in practical calculations of the SLMCPR.
Step 4: Using the ECPR probability distribution set forth in block 708, generated by Equations 1 and 2 shown above, determine the percentage of NRSBT in the core by summing the probabilities of each rod in the core that is subject to boiling transition, as shown by block 704. This summation is performed using Equation 3, shown above.
Step 5: Vary the parameters set forth in blocks 706 and 707 for a set number of Monte Carlo statistical trials, as shown by block 705. Compile the statistics from all the trials from steps 2 through 4 to generate a probability distribution of NRSBT.
Step 6: Compare the value of percentage of NRSBT to 0.1%, as shown in block 709. If the percentage is greater than 0.1%, reset the core parameters to different initial conditions in order to comply with the USNRC regulations, as shown in block 710. Similar to Step 1 and block 701, the new initial conditions are assumed to generate the SLMCPR. The determination of NRSBT loops until the value of NRSBT is equal to 0.1%. Similarly, if the percentage is less than 0.1%, the core parameters are reset to increase the value of NRSBT in order to operate the core more efficiently.
Step 7: If the percentage of NRSBT equals 0.1%, the assumed value of SLMCPR, which equals core MCPR, is the limit at which the core may operate, as shown by block 711.
Step 8: Since this process includes relatively uncertain simulations in steps 2 and 3, as shown by blocks 702 and 703, the change in CPR is evaluated at a 95% confidence interval, xcex94CPR95/95. The OLMCPR equals the linear addition of the SLMCPR to the xcex94CPR95/95. The resulting value of the OLMCPR complies with the USNRC regulations.
Motivated by the difficulties in calculating OLMCPR directly and the overly conservative approximation technique currently used, the inventors were led to examine more closely some of the processes conventionally used in evaluating BWR designs and calculating OLMCPR. For example, the following is a brief list summarizing two of the most prominent factors identified by the inventors as constraining the ability to calculate OLMCPR directly using the ideal method:
1. The number of calculations necessary to evaluate each AOO would be too cumbersome. To establish a statistically sound estimation of the NRSBT, approximately one hundred trials for each AOO would have to be performed. The currently-available equipment has inherent limitations that prevent the requisite number of transient calculations from being performed within the necessary timeframe.
2. The currently-available equipment cannot simulate local power distribution or the relative position of the rod within the fuel bundle (R-factor). The variations within each rod bundle are essential to compute an accurate NRSBT. Without a precise method of estimating the effects of the variations, a direct calculation of OLMCPR would be unavoidably inaccurate.
Due to the excessive degree of conservatism inherent in the conventional basis used for evaluation of BWR operations, a substantial increase in the operating margin for a BWR can be realized by using other approaches toward determining the OLMCPR. Applicants have developed a mathematically-sound approach to determining OLMCPR that allows for a substantial increase in the permissible operating margin for a reactor and increased operating efficiency, greater fuel generation and/or lowered fuel exhaustion. For example, demonstrating that a particular reactor or reactor design actually has a greater operational margin than may have been previously realized, e.g., due to the use of an unnecessarily conservative evaluation method, could permit operation at increased output power levels or at comparable power output levels using less fuel. Accordingly, a more mathematically-sound evaluation method that results in a substantially greater operational margin for Boiling Water Reactors is presented herein for calculating and demonstrating the OLMCPR.
Briefly, the improved method of the present invention is based on producing a histogram of the number of reactor fuel rods susceptible to operation at xe2x80x9cboiling transitionxe2x80x9d temperatures over a range of variations in selected parametric quantities that are indicative of reactor design constraints and operating conditions. In addition, a core operational modeling approach using predetermined PDFs of the change in critical power ratio (xcex94CPR/ICPR) for each type of transient event specific to the type of BWR is employed for simulating BWR thermal hydraulics and neutron kinetics during an xe2x80x9canticipated operational occurrencexe2x80x9d or AOO in the reactor (for example, a operational occurrence that causes a brief power transient). Basically, in the present invention, all model and reactor plant parameters that may affect the number of rods subject to boiling transition (NRSBT) are taken into account in projecting the PDF of the NRSBT. The NRSBT is then evaluated statistically in order to determine the OLMCPR directly without the need for first calculating a value for the SLMCPR. Using this approach, the present invention achieves a direct evaluation of OLMCPR of the reactor from a statistical analysis of histograms for the transient conditionxe2x80x94as opposed the conventional xe2x80x9cindirectxe2x80x9d approach of determining an OLMCPR from a combination of values obtained by separately evaluating both a steady-state SLMCPR and the change in the critical power ratio (xcex94CPR) due to a transient operational occurrence.